Abstract

We introduce a class of univalent functions
Rn(λ,α) defined by a new differential operator
Dnf(z), n∈ℕ0={0,1,2,…}, where
D0f(z)=f(z), D1f(z)=(1−λ)f(z)+λzf′(z)=Dλf(z), λ≥0, and
Dnf(z)=Dλ(Dn−1f(z)). Inclusion relations,
extreme points of Rn(λ,α), some convolution
properties of functions belonging to Rn(λ,α), and
other results are given.

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